Pericyclic reactions a mechanistic and problem solving approach

Pericyclic Reactions
A Mechanistic and Problem-Solving Approach

Sunil Kumar
Department of Chemistry
F.G.M. Govt. College
Haryana, India

Vinod Kumar
Department of Chemistry
Maharishi Markandeshwar University
Haryana, India

S.P. Singh
Department of Chemistry
Kurukshetra University, Kurukshetra
Haryana, India

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To Our Families
Sunil Kumar
Parents
Dr. Meenakshi, Ayush, Neerav
Vinod Kumar
Parents
Sushma, Mohit, Vignesh
S.P. Singh
Pushpa, Sunny, Romy
Preeti, Preety
Poorva, Uday, Adi, Veer


Preface
Ever since the appearance of the classic The Conservation of Orbital Symmetry
by Woodward and Hoffmann in 1970, there has been a surge in the publication of
many books and excellent review articles dealing with this topic. This was
natural as after having established mechanisms of ionic and radical reactions,
focus had shifted to uncover the mechanisms of the so-called “no-mechanism
reactions.” The uncovering of the fact that orbital symmetry is conserved in
concerted reactions was a turning point in our understanding of organic reactions. It is now possible to predict the stereochemistry of such reactions by
following the simple rule that stereochemical consequences of reactions initiated
thermally will be opposite to those performed under photochemical conditions.
Study of pericyclic reactions, as these are known today, is an integral part of our
understanding of organic reaction mechanisms.
Despite the presence of many excellent books on this vibrant topic, there was
an absence of a book that concentrates primarily on a problem-solving approach
for understanding this topic. We had realized during our teaching career that the
most effective way to learn a conceptual topic is through such an approach. This
book is written to fill this important gap in the belief that it would be helpful to

students to have problems pertaining to different types of pericyclic reactions
compiled together in a single book.
The book opens with an introduction (Chapter 1), which, besides providing
background information needed for appreciating different types of pericyclic
reactions, outlines simple ways to analyze these reactions using orbital symmetry correlation diagram, frontier molecular orbital (FMO), and perturbation
molecular orbital (PMO) methods. This chapter also has references to important
published reviews and articles.
Electrocyclic, sigmatropic, and cycloaddition reactions are subsequently
described in Chapters 2, 3, and 4, respectively. Chapter 5 is devoted to a study of
cheletropic and 1,3-dipolar cycloaddition reactions as examples of concerted
reactions. Many group transfer reactions and elimination reactions, including
pyrolytic reactions, are included in Chapter 6. There are solved problems in each
chapter that are designed for students to develop proficiency that can be acquired
only by practice. These problems, about 450, provide sufficient breadth to be
adequately comprehensive. Solutions to all these problems are provided in each
chapter. Finally, in Chapter 7, we have compiled unworked problems whose

xi


xii

Preface

solutions are provided separately in the Appendix. The aim behind introducing
these unsolved problems is to let the students develop their own skills.
Assuming that a student has taken courses in organic chemistry that include
reaction mechanisms and stereochemistry, the book is meant to be taught as a
one-semester course to graduate and senior undergraduate students majoring in
chemistry. One has to remember that a book designed for a one-semester course

cannot include all the reactions reported in the literature; rather, only representative examples of each of various reaction types are given. A general index is
included, which it is hoped will be of help to readers in searching for the types of
reactions related to a particular problem.
We hope that our book will be well received by students and teachers.
We encourage all those who read and use this book to contact us with any
comments, suggestions, or corrections for future editions. Our email addresses
are: , , and shivpsingh@
rediffmail.com.
We thank our reviewers for carefully reading the manuscript and offering
valuable suggestions. Finally, we thank the editorial staff of Elsevier for bringing
the book to fruition.
July 2015

Sunil Kumar
Vinod Kumar
S.P. Singh


Chapter 1

Pericyclic Reactions and
Molecular Orbital Symmetry
Chapter Outline
1.1 Classification of Pericyclic
Reactions
1.2 Molecular Orbitals of
Alkenes and Conjugated
Polyene Systems
1.3 Molecular Orbitals
of Conjugated Ions

or Radicals
1.4 Symmetry Properties of p or
s-Molecular Orbitals

2

3

7
11

1.5 Analysis of Pericyclic
Reactions
1.5.1 Orbital Symmetry
Correlation Diagram
Method
1.5.2 Frontier Molecular
Orbital Method
1.5.3 Perturbation Molecular
Orbital Method
Further Reading

13

13
15
17
19

In organic chemistry, a large number of chemical reactions containing multiple

bond(s) do not involve ionic or free radical intermediates and are remarkably
insensitive to the presence or absence of solvents and catalysts. Many of these
reactions are characterized by the making and breaking of two or more bonds
in a single concerted step through the cyclic transition state, wherein all firstorder bondings are changed. Such reactions are named as pericyclic reactions
by Woodward and Hoffmann.
The word concerted means reactant bonds are broken and product bonds
are formed synchronously, though not necessarily symmetrically without the
involvement of an intermediate. The word pericyclic means the movement of
electrons (p-electrons in most cases) in a cyclic manner or around the circle
(i.e., peri ¼ around, cyclic ¼ circle or ring).
They are initiated by either heat (thermal initiation) or light (photo
initiation) and are highly stereospecific in nature. The most remarkable
observation about these reactions is that, very often, thermal and photochemical processes yield products with different stereochemistry. Most of
these reactions are equilibrium processes in which direction of equilibrium
depends on the enthalpy and entropy of the reacting species. Therefore, in
general, three important points that should be considered while studying the
Pericyclic Reactions. />Copyright © 2016 Elsevier Inc. All rights reserved.

1


2

Pericyclic Reactions

pericyclic reactions are: involvement of p-electrons, type of activation energy
required (thermal or light), and stereochemistry of the reaction.
There is a close relationship between the mode of energy supplied and
stereochemistry for a pericyclic reaction, which can be exemplified by
considering the simpler reactions shown in Scheme 1.1.

SCHEME 1.1 Stereochemical changes in pericyclic reactions under thermal and photochemical
conditions.

When heat energy is supplied to the starting material, then it gives one
isomer, while light energy is responsible for generating the other isomer from
the same starting material.

1.1 CLASSIFICATION OF PERICYCLIC REACTIONS
Pericyclic reactions are mainly classified into the four most common types of
reactions as depicted in Scheme 1.2.

SCHEME 1.2 Common types of pericyclic reactions.

In an electrocyclic reaction, a cyclic system (ring closure) is formed
through the formation of a s-bond from an open-chain conjugated polyene
system at the cost of a multiple bond and vice versa (ring opening). These
reactions are unimolecular in nature as the rate of reactions depends upon the


Pericyclic Reactions and Molecular Orbital Symmetry Chapter j 1

3

presence of one type of reactant species. Such reactions are reversible in
nature, but the direction of the reaction is mainly controlled by thermodynamics. Most of the electrocyclic reactions are related to ring closing process
instead of ring opening due to an interaction between the terminal carbon
atoms forming a s-bond (more stable) at the cost of a p-bond.
Sigmatropic rearrangements are the unimolecular isomerization reactions
in which a s-bond moves from one position to another over an unsaturated system.

In such reactions, rearrangement of the p-bonds takes place to accommodate the
new s-bond, but the total number of p-bonds remains the same.
In cycloaddition reactions, two or more components containing p-electrons
come together to form the cyclic system(s) through the formation of two or
more new s-bonds at the cost of overall two or more p-bonds, respectively, at
least one from each component. Amongst the pericyclic reactions, cycloadditions are known as the most abundant, featureful, and valuable class of the
chemical reactions. The reactions are known as intramolecular when cycloaddition occurs within the same molecule. The reversal of cycloaddition in the
same manner is known as cycloreversion. There are some cycloaddition
reactions that proceed through the stepwise ionic or free radical mechanism and
thus are not considered as pericyclic reactions.
These reactions are further extended to cheletropic and 1,3-dipolar
reactions, which shall be discussed in detail in Chapter 5.
Group transfer reactions involve the transfer of one or more atoms or
groups from one component to another in a concerted manner. In these
reactions, two components join together to form a single molecule through the
formation of a s-bond.
It is very important to note that in studying the pericyclic reactions, the curved
arrows can be drawn in clockwise or anticlockwise direction (Scheme 1.3). The
direction of arrows does not indicate the flow of electrons from one component or
site to another as in the case of ionic reactions; rather, it indicates where to draw
the new bonds.

SCHEME 1.3 Clockwise and anticlockwise direction of the curved arrows in pericyclic
reactions.

1.2 MOLECULAR ORBITALS OF ALKENES AND
CONJUGATED POLYENE SYSTEMS
In order to understand and explain the results of the various pericyclic reactions on the basis of different theoretical models, a basic understanding of
the molecular orbitals of the molecules, particularly those of alkenes and
conjugated polyene systems and their symmetry properties, is required.

4

Pericyclic Reactions

According to the molecular orbital theory, molecular orbitals (MOs) are
formed by the linear combination of atomic orbitals (LCAO) and then filled
by the electron pairs. In LCAO when two atomic orbitals of equivalent
energy interact, they always yield two molecular orbitals, a bonding and a
corresponding antibonding orbital. The bonding orbital possesses lower
energy and more stability while antibonding possesses higher energy and less
stability as compared to an isolated atomic orbital. Let us consider the
simplest example of H2 molecule formed by the combination of 1s atomic
orbitals (Figure 1.1).
nodal plane

E

Eσ* (σ*) antibonding
1s
H

1s
Eσ

H

(σ) bonding
molecular orbitals

FIGURE 1.1 Formation of molecular orbitals in the case of an H2 molecule.

The bonding molecular orbital is a result of positive (constructive) overlap,
and hence electron density lies in the region between two nuclei. However, an
antibonding molecular orbital is formed as a result of negative (destructive)
overlap and, therefore, exhibits a nodal plane in the region between the two
nuclei. The bonding and antibonding molecular orbitals exhibit unequal
splitting pattern with respect to the atomic orbitals because a fully filled
molecular orbital has higher energy due to interelectronic repulsion.
We now consider molecular orbital theory with reference to the simplest
p-molecular system, ethene. As already discussed, the number of molecular
orbitals formed is always equal to the number of atomic orbitals combining
together. Similarly, in the case of an ethene molecule, sideways interaction
between p-orbitals of the two individual carbon atoms results in the formation
of the new p bonding and p* antibonding molecular orbitals that differ in
energy (Figure 1.2). In the bonding orbital of ethene, there is a constructive
overlap of two similar lobes of p-orbitals in the bonding region between the
nuclei. However, in the case of an antibonding orbital, there is destructive
overlap of two opposite lobes in the bonding region. Each p-orbital consists of
two lobes with opposite phases of the wave function.
We ignore s-bond skeleton in this treatment as sigma molecular orbitals
remain unaffected during the course of a pericyclic reaction.
The conjugated polyenes constitute an important class of organic
compounds exhibiting a variety of pericyclic reactions. On the basis of the


Pericyclic Reactions and Molecular Orbital Symmetry Chapter j 1

nodal plane

node
•
node

5

π*

antibonding
•
p-orbital

nodal plane E
π

p-orbital

p-orbital

bonding
Ethene
FIGURE 1.2 Formation of two molecular orbitals (p and p*) of ethene.

number of p-electrons, such compounds are classified into two categories
bearing 4n or (4n ỵ 2) p-electron systems. In order to construct the molecular
orbitals for such polyene systems, let us consider buta-1,3-diene as the
simplest example.
In the molecule of buta-1,3-diene, there are four p-orbitals located on four
adjacent carbon atoms and hence this generates four new p-molecular orbitals
on overlapping. The way to get these new p-molecular orbitals is the linear

combination of two p-molecular orbitals of ethene according to the
perturbation molecular orbital (PMO) theory. Like the combination of atomic
orbitals, overlapping of the bonding (s or p) or antibonding molecular orbitals
(s* or p*) of the reactants (here, ethene) results in the formation of the new
molecular orbitals that are designated as J1, J2, etc. in the product (here,
buta-1,3-diene).
According to PMO theory, linear combination always takes place between
the two orbitals (two molecular orbitals or two atomic orbitals, or one atomic
and one molecular orbital) having minimum energy difference. Thus, here we
need to consider pep and p*ep* interactions (constructive or destructive)
instead of interactions between p and p* orbitals (Figure 1.3). In buta1,3-diene, 4p-electrons are accommodated in the first two p-molecular orbitals, and the remaining two higher energy p-molecular orbitals will remain
unoccupied in the ground state of the molecule.
The lowest energy orbital (represented as wave function J1) of buta1,3-diene does not have any node and is the most stable due to the presence of
three bonding interactions. However, the second molecular orbital J2
possesses one node, two bonding and one antibonding interactions, and would
be less stable than J1. The J3 has two nodes and one bonding interaction.
Due to the two antibonding interactions, J3 possesses overall antibonding
character and thus energy of this orbital is more than the energy of J2. The J4
orbital is formed by the interaction between p* and p* of two ethene molecules. It bears three nodes and the highest energy.
Similarly, in the case of longer conjugated systems like a hexa-1,3,5-triene
system, there are six p-orbitals on six adjacent carbon atoms, which can


6

Pericyclic Reactions

Ψ4 = π∗ − π∗
3 nodes, 0 bonding interaction

π∗

Ψ3 = π∗ + π∗

LUMO

π∗

2 nodes, 1 bonding interaction

E

Ψ2 = π − π

HOMO
1 node, 2 bonding interactions

π
Ethene

π
Ethene

Ψ1 = π + π
most stable, 0 node,
3 bonding interactions
Buta-1,3-diene
FIGURE 1.3 Formation of p-molecular orbitals in buta-1,3-diene.

generate six new p-molecular orbitals (Figure 1.4). In hexa-1,3,5-triene, 6pelectrons are accommodated in the first three bonding p-molecular orbitals

(J1, J2, J3) and the remaining three higher energy antibonding p-molecular
orbitals (J4, J5, J6) will remain unoccupied in the ground state.
On the basis of molecular orbital diagrams of ethene, buta-1,3-diene, and
hexa-1,3,5-triene, the following points should be considered while constructing the molecular orbitals of the conjugated polyenes:
1. Consider only p-molecular orbitals and ignore s-bond skeleton as sigma
molecular orbitals remain unaffected during the course of a pericyclic
reaction.
2. For a system containing n p-electrons (n ¼ even), interaction of p-orbitals
leads to the formation of n/2 p-bonding and n/2 p-antibonding molecular
orbitals.
3. The bonding molecular orbitals are filled by the electrons, while antibonding orbitals remain vacant in the ground state of the molecule.
4. The lowest energy molecular orbital (for example, J1 in the case of buta1,3-diene) always has no node, however, the next higher has one node and
the second higher has two nodes and so on. Thus, the nth molecular orbital
will have n À 1 nodes.


Pericyclic Reactions and Molecular Orbital Symmetry Chapter j 1

7

Ψ6
5 nodes, 0 bonding interaction

antibonding
M. O.

Ψ5
4 nodes, 1 bonding interaction

Ψ4

LUMO
3 nodes, 2 bonding interactions
E

Ψ3
2 nodes, 3 bonding interactions

HOMO

bonding
M. O.

Ψ2
1 node, 4 bonding interactions

Ψ1
most stable, 0 node, 5 bonding interactions
Hexa-1,3,5-triene
FIGURE 1.4 p-Molecular orbitals in a hexa-1,3,5-triene system.

5. It is important to note that the nodes are found at the most symmetric points
in a molecular orbital. For example, in the case of J2 of buta-1,3-diene, a
node is present at the center of C2eC3 bond, however, it will be incorrect if
the node is present at the center of a C1eC2 bond or C3eC4 bond.

1.3 MOLECULAR ORBITALS OF CONJUGATED IONS OR
RADICALS
The construction of molecular orbitals in the case of conjugated p-systems
having an odd number of carbons can be made in a similar manner. Some
important examples of this class include cation or anion or free radical of

8

Pericyclic Reactions

propenyl-, pentadienyl-, and heptatrienyl-like systems. Such systems, in
addition to bonding and antibonding orbitals, possess a nonbonding molecular
orbital in which nodal planes pass through the carbon atoms.
Let us first consider the case of an allylic system bearing cation or anion or
free radical character. In an allylic system, three new molecular orbitals can be
generated by a linear combination of one molecular orbital of ethene
component and an isolated p-orbital of the carbon atom. As per PMO theory,
in the allylic system linear combination takes place between one ethene molecular orbital and one p-orbital, and thus we need to consider the results of
pep and p*ep orbital interactions only. The linear combination of p with
p-orbital in a bonding manner (with the signs of the wave function of the two
adjacent atomic orbitals matching) yields a new molecular orbital having least
energy, i.e., J1, while in antibonding manner (with the signs of the wave
function of the two adjacent atomic orbitals unmatched) this gives another new
molecular orbital having more energy i.e., J20 . In a similar way, interaction of
p* with p-orbital in a bonding as well as antibonding manner yields two new
molecular orbitals, one having low energy, i.e., J200 , and another having higher
energy, i.e., J3 (Figure 1.5).

Ψ∗3 = π∗ − p
π∗

Ψ2' = π − p
E
Ψ2'' = π∗ + p

p-orbital

π
Ethene

Ψ1 = π + p
Allylic system

FIGURE 1.5 Mixing of p-orbital with molecular orbitals of ethene in an allylic system.

However, we cannot get four orbitals by using three orbitals. In fact, we do
not get two separate orbitals J20 and J200 but something in between, namely
J2. The orbital J2 can be created by adding J20 and J200 so that they cancel
each other on Ce2 and reinforce each other on Ce1 and Ce3. Thus J2 can be
considered as a combination of J20 and J200 , which is formed by mixing the
p-orbital in an antibonding manner and with the p*-orbital in a bonding


Pericyclic Reactions and Molecular Orbital Symmetry Chapter j 1

9

manner. In case of J2, a nonbonding molecular orbital, a node is always
present at the central carbon of the system. This means that there is no
p-electron density at the central carbon atom. Moreover, the energy of a
nonbonding molecular orbital is the same as the contributing atomic orbitals.
Hence, there is no net stabilization as a result (Figure 1.6).

Ψ3∗= π∗ − p

π∗

antibonding
M. O.

Ψ2 = Ψ2' + Ψ2''

E

nonbonding
M. O.

p-orbital

π
Ethene

Ψ1 = π + p
Allylic system
bonding M. O.

FIGURE 1.6 Mixing of p-orbital with molecular orbitals of ethene in an allylic system
continued.

As illustrated in Figure 1.6, the following points need to be considered
while constructing the molecular orbital diagram of a conjugated open-chain
system having an odd number of carbon atoms.
1. In case of conjugated p-systems having an odd number of n carbon atoms,
n number of molecular orbitals are present.
2. The system will have (n À 1)/2 bonding, (n À 1)/2 antibonding, and one

nonbonding molecular orbital.
3. The nonbonding molecular orbital will be (n ỵ 1)/2nd orbital and always
lies between the bonding and antibonding molecular orbitals.
4. All nodal planes (n À 1) pass through the carbon atom(s) of the
nonbonding molecular orbitals (Jn).
5. All nodal planes pass between two carbon nuclei in case of odd Jn (J1,
J3, J5, so on) while one nodal plane passes through the central carbon
atom and remaining nodal planes pass between two carbon atoms in case of
even Jn (J2, J4, J6, so on).
The molecular orbital diagrams for propenyl and pentadienyl systems are
illustrated in Figure 1.7 in which the molecular orbitals for their corresponding


10

Pericyclic Reactions

Ψ5
antibonding M. O.
Ψ3
antibonding M. O.

E Ψ2

Ψ4

Ψ3

nonbonding M. O.

nonbonding M. O.
Ψ2

Ψ1
bonding M. O.
Propenyl system

bonding M. O.
Ψ1
Pentadienyl system

FIGURE 1.7 Molecular orbitals of propenyl and pentadienyl systems.

cation or anion or carbon free radical remain the same. The cation or anion or
free radical species differ in number of electrons (electron occupancy) that are
filled according to Aufbau’s rule in their ground state as shown in Figure 1.8.
Also, Hund’s rule and the Pauli exclusion principle should be followed.

FIGURE 1.8 Electron occupancy diagram of propenyl, pentadienyl, and heptatriene systems.


Pericyclic Reactions and Molecular Orbital Symmetry Chapter j 1

11

1.4 SYMMETRY PROPERTIES OF p OR s-MOLECULAR
ORBITALS
There are two independent symmetry elements, viz., mirror plane, m, and
twofold axis, C2, that are used to characterize various molecular orbitals of
alkenes or conjugated polyene systems.

1. Symmetry about a mirror plane (m) bisects the molecular orbital in such a
way that lobes of the same color or sign are reflected, and, therefore,
reflections on either side of the plane are identical. It is perpendicular to the
plane of the atoms.
2. Symmetry about a twofold axis (C2) passing at right angles in the same plane,
and through the center of the framework of the atoms forming the molecular
orbital is said to be present if the rotation of the molecule around the axis by
180 (360 /2) results in a molecular orbital identical with the original.
Let us examine symmetry properties of p-orbitals of ethene in the ground
state and also in the excited state. The ground state (p) orbital is symmetric
(S) with respect to the mirror plane, m, and antisymmetric (A) with respect to
rotation axis, C2. On the other hand, the antibonding orbital (p*) of ethene is
antisymmetric with respect to m and symmetric with respect to the C2 axis.
However, the sigma orbital of a CeC covalent bond has a mirror plane symmetry,
and since a rotation of 180 through its midpoint regenerates the same sigma
orbital, it also has C2 symmetry. A s* orbital is antisymmetric with respect to
both m and C2. The symmetry properties of these MOs (bonding or antibonding)
are shown in Figures 1.9 and 1.10, and are summarized in Table 1.1.

π*

π*
C2

C2
σ

C2

π

π
C2

σ

C2
C2 symmetric orbitals

C2
σ*

C2

σ*

C2
C2 antisymmetric orbitals

FIGURE 1.9 Twofold axis (C2) symmetric and antisymmetric molecular orbitals.

π
m

m
m symmetric orbitals

σ

π∗

m
m
m antisymmetric orbitals

FIGURE 1.10 Mirror plane (m) symmetric and antisymmetric molecular orbitals.

σ∗


TABLE 1.1 Symmetry properties of the s and p-molecular orbitals;
A ¼ antisymmetric, S ¼ symmetric.
Orbitals

m

C2

Orbitals

m

C2

p

S

A

s

S

S

p*

A

S

s*

A

A

Ψ6 (m-A; C2-S)

Ψ4 (m-A; C2-S)
Ψ5 (m-S; C2-A)

Ψ3 (m-S; C2-A)
Ψ4 (m-A; C2-S)
E

Ψ2 (m-A; C2-S)

Ψ3 (m-S; C2-A)

Ψ2 (m-A; C2-S)
Ψ1 (m-S; C2-A)
Butadiene

Ψ1 (m-S; C2-A)
Hexatriene
FIGURE 1.11 Symmetry properties of the molecular orbitals of butadiene and hexatriene systems.


Pericyclic Reactions and Molecular Orbital Symmetry Chapter j 1

13

A similar consideration leads to the following symmetry properties for the
four p-molecular orbitals of butadiene and six p-molecular orbitals of hexatriene and are summarized in Figure 1.11.
In conclusion, for a linear conjugated p-system, the wave function Jn will
have n À 1 nodes. When n À 1 is zero or an even integer, Jn will be
symmetric with respect to mirror plane (m) and antisymmetric with respect to
C2. When n À 1 is an odd integer, Jn will have the symmetry exactly reversed
(Table 1.2).
TABLE 1.2 Symmetry elements in the orbital Jn of a linear conjugated
p-system.
Wave functions

Nodes (n À 1)

m

C2

Jodd

0 or Even integer

S

A

Jeven

Odd integer

A

S

1.5 ANALYSIS OF PERICYCLIC REACTIONS
Pericyclic reactions have been known for a long time, but it was in 1965 when
Woodward and Hoffmann offered a reasonable explanation for them based on
the principle of the “Conservation of Orbital Symmetry.” The principle states
that orbital symmetry is conserved in the concerted reactions. Molecular
orbitals in the reactant can only transform into those orbitals in the products
that have the same symmetry properties with respect to the elements of
symmetry preserved in the reaction. Even if symmetry is slightly disturbed in a
reactant by a trivial substituent or by asymmetry of the molecule, a concerted
reaction may still be analyzed by mixing the interacting orbitals according to
quantum mechanical principles and following them through the reaction. The
energy of the transition state of a symmetry allowed process will necessarily
be lower than that of the alternative symmetry forbidden path, and even when
this difference is small, a concerted reaction will take the path of least resistance, i.e., the symmetry allowed path, if that path is available.

Another explanation has been proposed by K. Fukuii on the basis of
frontier molecular orbitals (HOMOeLUMO) of the substrates; this method is
known as the frontier molecular orbitals (FMO) method. Alternatively, the
PMO theory based on the WoodwardeHoffmann rule and Huăckel-Moăbius
method is also used to explain the results of pericyclic reactions.

1.5.1 Orbital Symmetry Correlation Diagram Method
The orbital symmetry correlation diagram method was developed by Woodward and Hoffmann and extended by Longuet-Higgins and Abrahamson.


14

Pericyclic Reactions

The most important observation in the study of pericyclic reactions is the
existence of conservation of molecular orbital symmetry throughout the
transformation, meaning thereby that the symmetric orbitals are converted into
symmetric orbitals whereas antisymmetric orbitals are converted into antisymmetric orbitals. In this approach, symmetry properties of various molecular orbitals of the bonds that are involved in the bond breaking and formation
process during the reaction are considered and identified with respect to C2
and m elements of symmetry. These properties remain preserved throughout
the course of reaction. Then a correlation diagram is drawn in which the
molecular orbital levels of like symmetry of the reactant are related to that of
the product by drawing lines.
In the ground state, if the symmetry of MOs of the reactant matches that of
the products that are nearest in energies, then reaction is thermally allowed.
However, if the symmetry of MOs of the reactant matches that of the product
in the first excited state but not in the ground state, then the reaction is
photochemically allowed (Figure 1.12). When symmetries of the reactant and
product molecular orbitals differ, the reaction does not occur in a concerted
manner. It must be noted that a symmetry element becomes irrelevant when

orbitals involved in the reaction are all symmetric or antisymmetric. In
conclusion, we can say that in pericyclic transformations, symmetry properties
of the reactants and products remain conserved.

FIGURE 1.12
conditions.

Correlation between reactant and product MOs under thermal and photochemical

While drawing the orbital correlation diagram for any system, the
following points must be considered:
1. Each reactant molecule must be converted into simpler analogue by removing
the substituents attached, if any, because substituent affects only the energy
levels of MOs and not the symmetry properties of the p-system. Let us
consider the DielseAlder reaction, a [4 ỵ 2] p-system (Scheme 1.4).

SCHEME 1.4 Conversion of the reactant molecules into simpler analogue.


Pericyclic Reactions and Molecular Orbital Symmetry Chapter j 1

15

2. Different processes must be treated separately even if they occur within the
same molecule because simultaneous consideration may lead to erroneous
outcome. For example, hypothetical two [2 ỵ 2] cycloaddition reactions in
cyclooctatetraene have to be considered separately. Similarly, in hexa2,4-diene, conrotatory and disrotatory electrocyclization processes have to
be treated separately while making the orbital diagram (Scheme 1.5).

SCHEME 1.5 Independent processes occurring in the same molecule.

3. Draw and identify the orbitals undergoing change.
4. Arrange the orbitals in order of their increasing energies, and draw them
for reactant on left and for product on the right side.
5. Symmetry properties of the various molecular orbitals of the bonds being
involved in breaking and formation process during the reaction are
considered and identified with respect to elements of symmetry (C2 and s)
that are preserved throughout the reaction.
6. Orbitals of same symmetry do not cross in the correlation diagram as per
non-cross rule.
7. After assigning the symmetry element to each orbital, construct an orbital
correlation diagram by connecting the orbitals of starting materials to those
of the product nearest in energy and having same symmetry.
8. If heteroatoms are present in an alkene component, they have to be
replaced by carbon analogues. Interactions in such systems should be
considered carefully as they may generate the possibilities of new reaction
either by nonbonding electrons or by availability of low energy LUMO.

1.5.2 Frontier Molecular Orbital Method
Although it is more fruitful to construct a correlation diagram for the detailed
analysis of a pericyclic reaction, there is, nevertheless, an alternative method
that also enables us to reach similar conclusions. It is an easy and extremely
simple approach that is based on the interaction of the frontier orbitals, i.e., the
highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) of the components that are involved in a pericyclic
reaction.
As shown in Figure 1.13, irradiation of an alkene or conjugated polyene
system promotes an electron from its ground state HOMO to the ground state
LUMO, which then becomes the highest occupied molecular orbital in the
excited state, for example, J3 of butadiene becomes HOMO upon excitation
of an electron from J2 to J3 on irradiation.

16

Pericyclic Reactions

FIGURE 1.13 HOMO and LUMO of alkene systems.

The explanation for this alternative approach is based on the fact that
overlapping of wave functions of the same sign is essential for the bond formation. When two systems come close to each other, then their unperturbed
molecular orbitals start to interact and those that are close in energy interact
more strongly than other orbitals. It is well known that interaction of two filled
MOs does not lead to the net energy stabilization of the system but it is the
interaction between one filled and other vacant MO that leads to net energy
stabilization. This explains why interaction between HOMO and LUMO is
considered in this approach (Figure 1.14). If interaction between these two
MOs is of bonding type (overlapping of same signed wave functions) in the
ground state, then reaction is thermally allowed. However, if it is of antibonding type (overlapping of opposite signed wave functions) then it is a
thermally forbidden reaction. On the other hand, if interaction between
HOMOeLUMO is of bonding type in the excited state, then reaction is
photochemically allowed. However, it is a photochemically forbidden reaction
when it is of antibonding type.
In order to apply the FMO approach in unimolecular pericyclic reactions
like electrocyclic reactions and sigmatropic rearrangements, we have to treat a
single molecule as having separate components. In such a case, only HOMO of
the component has to be considered to predict the feasibility of the reaction
under given conditions. Furthermore, this theory does not tell why the energy
barrier to forbidden reactions is so high.

bonding

bonding

antibonding

FIGURE 1.14 Interactions in FMOs of alkenes.

bonding

bonding


Pericyclic Reactions and Molecular Orbital Symmetry Chapter j 1

17

1.5.3 Perturbation Molecular Orbital Method
There is yet another qualitative molecular orbital approach, developed by
M.J.S. Dewar, that yields simple mnemonics to predict the same stereochemical variations in pericyclic reactions as do the other methods. In the
PMO method, aromatic or antiaromatic character of the cyclic transition state
is explained by considering the Huăckel-Moăbius concept of aromaticity. In a
Huăckel-type system, a cyclic array of all the interacting p-orbitals shares a
common nodal plane. A Huăckel system is aromatic (stabilized by cyclic
delocalization) when (4n ỵ 2) p-electrons are present, and antiaromatic
(destabilized by cyclic delocalization) when 4n p-electrons are present.
However, in a Moăbius-type system an extra node is present, introduced by
twisting the set of orbitals so that each one forms an angle, theta, with its
neighbors. In a Moăbius-type system, the molecules and transition states require
4n p-electrons for aromaticity and are antiaromatic with the usual (4n ỵ 2) pelectrons. It can be generalized and shown that a cyclic array of orbitals with
zero or an even number of sign inversions belongs to the Huăckel system, and

those with an odd number of sign inversions belong to the Moăbius system.
Application of this method to pericyclic reactions led to the generalization
that thermal reactions take place via aromatic or stable transition states
whereas photochemical reactions proceed via antiaromatic or unstable transition states. This is the case because a controlling factor in photochemical
processes is conversion of excited state reactants into ground state products.
Thus, the photochemical reactions convert the reactants into the antiaromatic
transition states that correspond to forbidden thermal pericyclic reactions and
so lead to corresponding products.
In this approach, we have only to consider a cyclic array of interacting
atomic orbitals, representing those orbitals that undergo change in the transition state without considering the symmetry properties and assign signs to
the wave functions in the best manner for overlap. Finally, the number of
nodes in the array and the number of electrons involved are counted. It should
be noted that while counting the number of nodes we ignore sign inversions
within any of the basis orbitals (for example, as within a p-orbital). The
following examples illustrate the construction of orbital interaction diagrams
for the [2 ỵ 2] and [4 ỵ 2] cycloadditions by supraesupra and supraeantara
modes. (For a detailed description of these terms, refer to Chapter 4). Whether,
the reactions are allowed or not are predicted as follows. In the case of
[p2s ỵ p2s] cycloaddition (4n p-electron system), a supraesupra mode of
addition leads to a Huăckel array, which is antiaromatic with 4n p-electrons
(Figure 1.15). Therefore, the supraesupra mode of reaction is thermally
forbidden. However, a supraeantara mode of addition uses a Moăbius array,
which is aromatic with 4n p-electrons. Therefore, the reaction is thermally
allowed in this mode. Similarly, we can analyze the [p4s ỵ p2s] cycloaddition
having (4n ỵ 2) p-electrons (Figure 1.15). In this case, a supraesupra mode of
addition leads to a Huăckel array, which is aromatic with (4n þ 2) p-electrons.
Therefore, [p4s þ p2s] cycloaddition reaction now becomes thermally


18

Pericyclic Reactions

allowed. However, a [p4s ỵ p2a] cycloaddition uses a Moăbius array, which is
antiaromatic with (4n ỵ 2) p-electrons. Therefore, the reaction is thermally
forbidden in this mode.

T. S. for [π2s + π2s] cycloaddition,
Hückel system, 0 node, 4 electrons,
antiaromatic, hv allowed

T. S. for [π4s + π2s] cycloaddition,
Hückel system, 0 node, 6 electrons,
aromatic, Δ allowed
FIGURE 1.15

T. S. for [π2s + π2a] cycloaddition,
Möbius system,1 node, 4 electrons,
aromatic, Δ allowed

T. S. for [π4s + π2a] cycloaddition,
Möbius system,1 node, 6 electrons,
antiaromatic, hv allowed

PMO approach for [2 ỵ 2] and [4 ỵ 2] cycloadditions.

WoodwardeHoffmann rules based on the perturbation molecular orbital
method are summarized in Table 1.3.
TABLE 1.3 WoodwardeHoffmann rules based on the perturbation
molecular orbital method.

No. of
electrons

No. of
nodes

T. State
type

Aromaticity

Feasibility

4n ỵ 2

0 or Even

Huăckel

Aromatic

D allowed, hv
forbidden

4n

0 or Even

Huăckel

Antiaromatic

D forbidden, hv
allowed

4n ỵ 2

Odd

Moăbius

Antiaromatic

D forbidden, hv
allowed

4n

Odd

Moăbius

Aromatic

D allowed, hv
forbidden


Pericyclic Reactions and Molecular Orbital Symmetry Chapter j 1

19

Therefore, the prediction of reaction feasibility under thermal or photochemical condition depends upon the extent of stabilization of a cyclic transition state as compared to an open-chain system. The stabilization or
destabilization depends upon the aromatic or antiaromatic character of a cyclic
transition state in the ground state.

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